Thanh D Nguyen^{1}, Shun Zhang^{1}, Ajay Gupta^{1}, Susan A Gauthier^{1}, and Yi Wang^{1}

The objective of this study was to develop a robust automated lesion change detection algorithm for MS. Our preliminary results in 30 patients show that our SDC algorithm achieves much higher sensitivity and specificity (99%/76%) compared to that obtained with off-the-shelf LPA algorithm (76%/27%).

**Lesion detection
algorithm**.
Given two images I_{1} and I_{2}, the signal
change d=I_{2}-I_{1} at voxel* i* is assumed to have Gaussian noise with mean µ and standard deviation σ, and SDC is formulated as a composite hypothesis test between two hypotheses: H_{0}
~ N(0,σ^{2}) and H_{1} ~ N(µ,σ^{2}), where N is the
normal distribution and µ≠0 is unknown mean. σ can be estimated from
the brain WM mask extracted from T1-weighted image with exclusion of large
lesions (Fig.1). Assuming µ>0 (positive change), the test statistic can be
derived from the log-likelihood ratio test: t_{i} = $$$\sum_{j=1}^N$$$
d_{ij}
where N is the number of observations at voxel *i*. The test statistic is then
compared with a threshold γ chosen to control the
probability of false positives: P_{FP} = P(t ≥ γ | H_{0}). This test provides the best detection
power for a given P_{FP} regardless of the unknown µ (uniformly most
powerful detector) (5).

Since only one observation d_{i} is available per voxel, we propose to
compute the test statistic t_{i} = max(t_{k},k $$$\in$$$ T_{i}) where T_{i} denotes a 3-neighborhood system of voxel *i* (Fig.2) purposely
chosen to match the currently accepted minimum lesion size requirement of 3 mm (3
voxels in 1 mm isotropic images) (6). Intuitively, this test statistic encodes
in probabilistic terms the expectation that a bright voxel on the subtraction
image is more likely considered “changed” if at least two of its neighbor voxels also have relatively
high signals.

**MRI experiments**.
Thirty MS
patients underwent 3T MRI twice (interval 267±104 days, range 15-410 days). FLAIR
images were automatically co-registered in the halfway space (7). The test
statistic for FLAIR subtraction image was computed and thresholded to generate
the change mask (Fig.1). A false positive rate PFP of 0.0001 was
chosen to achieve high lesion sensitivity, which means that about 50/500,000 WM
voxels may be incorrectly labeled as “changed”. To reduce the number of false
positives, constraints were imposed on lesion size (≥3 voxels), location (lesions
within 2 voxels of CSF border has to be connected to a lesion outside), and
intensity on 2nd FLAIR (>2 standard deviations above mean).

For comparison, LPA (http:// www.applied-statistics.de) (8) was used to compute the lesion masks for FLAIR images with mask subtraction as a change mask. Lesion changes less than 3 voxels were excluded.

**Statistical
analysis**. A neuroradiologist reviewed FLAIR and subtraction images with overlaid color boxes encompassing the detected
lesion changes (Fig.3). These were labeled as “true positive” or “false
positive”. The reader also reviewed the images outside of these boxes to count
the number of missed lesion changes (“false negative”) and unchanged lesions
(“true negative”).

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